aim: rationals w/ unlike denominators course: adv. alg. & trig. do now: aim: how do we add and...

Aim: Rationals w/ Unlike Denominators

Course: Adv. Alg. & Trig.

Do Now:

Aim: How do we Add and Subtract Algebraic Fractions that have

different denominators?

Method 2 Find the lowest

common denominator

Method 1 Find a common denominator

by multiplying the denominators

6

1

4

3

10

4

6

1

4

3

4

4

6

1

6

6

4

3

2464

24

4

24

18

12

11

24

22

6

1

4

3

2

2

6

1

3

3

4

3

126&4 isofLCD

12

2

12

9

12

11



Finding the LCD

Find the LCD

xy; yz 2x + 1; 4x2 - 1

LCD of Numbers

LCD of Variable Expressions

4 2 2

Each LCD includes all the factors of both denominators

4 2 2x x LCD of 4 & 6 LCD of 4x & 6x2

xy = x · yyz = y · z

LCD = x · y · z

(2x + 1) = (2x + 1) 4x2 – 1 = (2x +1)(2x - 1)

LCD = (2x + 1)(2x – 1)

2 2 3 12LCD 6 2 3

22 2 3 12LCD x x x

26 2 3x x x



Finding the LCD

yzxy

11

x

x

yzz

z

xy

11LCD = xyz

xyz

x

xyz

z

xyz

xz

yx

46

yx

4

1

6 LCD = 1(x – y)

1

14

1

6

yxyx

yx

1)(

14

)(1

)(6

yxyx

yx

)(1

4)(6

yx

yx

yx

yx

466



Finding the LCD

22

531

yxyx

x2 = x · xxy = x · yy2 = y · yLCD = x · x · y · y = x2y2

2

2

22

2

2

531

x

x

yxy

xy

xyy

y

x

22

2

22

2 53

yx

x

xyxy

xy

yx

y

22

22 53

yx

xxyy

Find the LCD x2y2



Finding the LCD

42

3

63

10

xx

3x-6 = 3(x-2) 2x-4 = 2(x-2)LCD = 3(x-2)2 = 6(x-2) = 6x - 12

3

3

)2(2

3

2

2

)2(3

10

xx

)2(2

3

)2(3

10

xx

3)2(2

9

2)2(3

20

xx

126

29

2)2(3

29

xx

Factor the Denominators

Find the LCD

LCD - 6(x-2)



Finding the LCD

183

4

362

xx

x

x2 – 36 = (x – 6)(x + 6) 3x – 18 = 3(x – 6) LCD = 3(x - 6)( x + 6)

)6(3

4

)6)(6(

xxx

x

6

6

)6(3

4

3

3

)6)(6(

x

x

xxx

x

Factor the Denominators

Find the LCD

3(x - 6)( x + 6)



Finding the LCD

x2 – 36 = (x – 6)(x + 6) 3x – 18 = 3(x – 6) LCD = 3(x - 6)( x + 6)

)6)(6(3

)6(4

)6)(6(3

3

xx

x

xx

x

)6)(6(3

)6(43

xx

xx

)6)(6(3

2443

xx

xx

)6)(6(3

24

xx

x

6

6

)6(3

4

3

3

)6)(6(

x

x

xxx

x



Application Problem

An electrical conductor is any piece of material that allows electricity to flow through it. Resistance is measured in units called OHMS. A resistor is an electrical conductor that is manufactured to have a certain resistance. If two resistors are connected in parallel, the the resistance of the combination R is given by the formula

where R1 and R2 are the resistances of the resistors. What is the effective resistance of a 30-ohm resistor and a 20-ohm resistor that are connected in parallel?

21

111

RRR

Parallel

flow

R1

R1

aim: rationals w/ unlike denominators course: adv. alg. & trig. do now: aim: how do we add and...

Documents